相关论文: Interpolating vector fields for near identity maps…

We find the density matrix corresponding to the vacuum state of a massless Dirac field in two dimensions reduced to a region of the space formed by several disjoint intervals. We calculate explicitly its spectral decomposition. The…

We present an analytic approximation model for non-rigid point set registration, grounded in the multivariate Taylor expansion of vector-valued functions. By exploiting the algebraic structure of Taylor expansions, we construct a structured…

This paper introduces the trajectory divergence rate, a scalar field which locally gives the instantaneous attraction or repulsion of adjacent trajectories. This scalar field may be used to find highly attracting or repelling invariant…

Interpolating between measures supported by polygonal or polyhedral domains is a problem that has been recently addressed by the semi-discrete optimal transport framework. Within this framework, one of the domains is discretized with a set…

We discuss the interplay between lagrangian distributions and connections in symplectic geometry, beginning with the traditional case of symplectic manifolds and then passing to the more general context of poly- and multisymplectic…

The theme of the article is the application of the Poincare section method for visual classification of attractors in the four-dimensional phase space; the purpose of the study is to introduce consideration of three-dimensional Poincare…

Learning interpretable and interpolatable latent representations has been an emerging research direction, allowing researchers to understand and utilize the derived latent space for further applications such as visual synthesis or…

We develop an approach to affine symplectic invariant geometry of Lagrangian surfaces by the method of moving frames. The fundamental invariants of elliptic Lagrangian immersions in affine symplectic four-space are derived together with…

Although it is important both in theory as well as in applications, a theory of Birkhoff interpolation with main emphasis on the shape of the set of nodes is still missing. Although we will consider various shapes (e.g. we find all the…

Let $X$ be a smooth polarized algebraic surface over the compex number field. We discuss the invariants obtained from the moduli stacks of semistable sheaves of arbitrary ranks on $X$. For that purpose, we construct the virtual fundamental…

We present an analog to classic potential theory on weighted graphs. With nodes partitioned into exterior, boundary and interior nodes and an appropriate decomposition of the Laplacian, we define discrete analogues to the trace operators,…

We review the method of symplectic invariants recently introduced to solve matrix models loop equations, and further extended beyond the context of matrix models. For any given spectral curve, one defined a sequence of differential forms,…

A Lagrangian method for the numerical simulation of the Kraichnan passive scalar model is introduced. The method is based on Monte--Carlo simulations of tracer trajectories, supplemented by a point-splitting procedure for coinciding points.…

We classify isomorphism-invariant random digraphs according to where randomness resides, namely, arcs, vertices, and vertices and arcs together which in turn yield arc random digraphs (ARD), vertex random digraphs (VRD) and vertex-arc…

For a sufficiently nice 2 dimensional shape, we define its approximating matrix (or patterned matrix) as a random matrix with iid entries arranged according to a given pattern. For large approximating matrices, we observe that the…

We propose an approach to the problem of global reconstruction of an orientation field. The method is based on a geometric model called "bisector line fields", which maps a pair of vector fields to an orientation field, effectively…

We present a method for learning neural representations of flow maps from time-varying vector field data. The flow map is pervasive within the area of flow visualization, as it is foundational to numerous visualization techniques, e.g.…

Basing on invariant properties of universal multifractals we propose a simple algorithm for interpolation of multifractal densities. The algorithm admits generalization to a multidimensional case. Analitically obtained are multifractal…

We discuss the local behaviour of vector fields in the plane $\R^2$ around a regular singular point, using recently introduced reduced normal forms, i.e. Poincar\'e and Lie renormalized forms [{\it Lett. Math. Phys.} {\bf 42} (1997),…

We study the reduction of non-autonomous regular Lagrangian systems by symmetries, which are generated by vector fields associated with connections in the configuration bundle of the system $Q\times\real\to\real$. These kind of symmetries…